A type of mathematical equation used, typically, to represent curves in a plane or in space of three dimensions. In principle, however, there is no limitation to any particular number of dimensions. A parameter is actually an independent variable. In elementary analytic geometry a curve in the xy plane is often studied, in the first instance, as the locus of an equation y = F(x) or G(x, y) = 0. The form y = F(x) is not adequate for the complete representation of certain curves, whereas the form G(x,y) = 0 may be adequate. The circle x2 + y2 − 16 = 0 affords an example. But the form G(x,y) = 0 is not always convenient. The parametric form x = f(t), y = g(t) is often the most convenient; it is often the naturally occurring form of representation of the curve. For the circle x2 + y2 − 16 = 0, one possible parametric representation is x = 4 cos t and y = 4 sin t.

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